We introduce 'formal methods' of mechanized reasoning from computer science to address two problems in auction design and practice: is a given auction design soundly specified, possessing its intended properties; and, is the design faithfully implemented when actually run? Failure on either...

Formal methods use computers to verify proofs or even discover new theorems. Interest in applying formal methods to problems in economics has increased in the past decade, but - to date - none of this work has been published in economics journals. This paper applies formal methods to a familiar...

Pillage games [Jordan, 2006, "Pillage and Property", JET] have two features that make them richer than cooperative games in either characteristic or partition function form: they allow power externalities between coalitions; they allow resources to contribute to coalitions' power as well as to...

Jordan [2006] defined ‘pillage games’, a class of cooperative games whose dominance operator represents a ‘power function’ constrained by monotonicity axioms. In this environment, he proved that stable sets must be finite. We bound their cardinality above by a Ramsey number and show this...

Jordan [2006, “Pillage and property”, JET] characterises stable sets for three special cases of ‘pillage games’. For anonymous, three agent pillage games we show that: when the core is non-empty, it must take one of five forms; all such pillage games with an empty core represent the same...

Jordan [2006] defined ‘pillage games’, a class of cooperative games whose dominance operator is represented by a ‘power function’ satisfying coalitional and resource monotonicity axioms. In this environment, he proved that stable sets must be finite. We use graph theory to reinterpret...